• Communications for Statistical Applications and Methods
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• 제9권2호
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• pp.315-324
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• 2002

For estimating the error variance under the relative squared error loss in two-way analysis of variance models, we provide a class of hierarchical Bayes estimators and then derive a subclass of the hierarchical Bayes estimators, each member of which dominates the best multiple of the error sum of squares which is known to be minimax. We also identify a subclass of non-minimax hierarchical Bayes estimators.

• East Asian mathematical journal
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• 제5권1호
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• The Journal of Advanced Prosthodontics
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• 제13권1호
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• pp.55-64
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• 2021

PURPOSE. To investigate the biomechanical effect of marginal bone resorption (MBR) on the mandibular mini implant (MI)-retained overdenture (MI-OD) on the edentulous model. MATERIALS AND METHODS. The experimental mandibular edentulous model was modified from a commercial model with 2 mm thick artificial soft tissue under denture base. Two MIs (Φ2.6 mm × 10 mm) were bilaterally placed between the lateral incisor and the canine area and attached with magnetic attachments. Three groups were set up as follows: 1) alveolar bone around the MI without MBR (normal group), 2) with MBR to 1/2 the length of the implant (resorption group), and 3) complete denture (CD) without MI (CD group). Strain around the MI, pressure near the first molar area, and displacement of denture were simultaneously measured, loading up to 50 N under bilateral/unilateral loading. Statistical analysis was performed using independent-samples t test and one-way ANOVA (α=.05). RESULTS. The strain around the MI with MBR was approximately 1.5 times higher than that without MBR. The pressure in CD was higher than in MI-ODs (P<.05), while there was no statistical difference between the normal and resorption group (P>.05). Similarly, the CD demonstrated a greater displacement of the denture base than did the MI-ODs during bilateral and unilateral loadings (P<.05). CONCLUSION. The strain around the MI with MBR was approximately 1.5 times higher than that without MBR. The pressure on posterior alveolar ridge and denture displacement of MI-ODs significantly decreased compared to CDs, even when MBR occurs. Bilateral balanced occlusion was recommended for MI-ODs, especially when MBR occurred.